| National cyclopaedia - 1884
...as stated by Euclid it is not a true axiom. It runs thus — 44 If a straight line meets two other **straight lines, so as to make the two interior angles on the same side of it, taken** j together, less than two right angles ; these straight lines, being continually produced, shall at... | |
| 1885
...as stated, AB would coincide with EF ; and thus is it proved that all right angles are equal.* Axiom **XII.: — " If a straight line meets two straight...together, less than two right angles, these straight** linos being continually produced, shall at length meet upon that side on which are the angles which... | |
| New Zealand Institute - 1886
...equivalence of the three forms of the parallel-axiom mentioned in my paper. Form (a), (Euclid's) is : — " **If a straight line meets two straight lines, so as to make the two interior angles on the same** I side of it taken together less than two right angles, these straight lines being continually produced... | |
| Benjamin Franklin Finkel - 1888 - 481 Seiten
...so as to make the two interior angles *For definitions of geometrical magnitudes, see Mensuration. **on the same side of it taken together less than two...lines being continually produced shall at length meet** on that side< on which are the angles which are less than, two right angles. An axiom must possess... | |
| 1890
...in what is generally called the twelfth, by some the eleventh " axiom :" " If a straight line meet **two straight lines so as to make the two interior...on the same side of it taken together less than two** right-angles, these straight lines, being continually produced, shall at length meet on that side on... | |
| Florian Cajori - 1890 - 400 Seiten
...consists in what is generally called the twelfth, by some the eleventh "axiom :" " If a straight line meet **two straight lines so as to make the two interior...on the same side of it taken together less than two** right-angles, these straight lines, being continually produced, shall at length meet on that side on... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 515 Seiten
...— Prove this proposition independently of Prop. 27. Ax. 12. — If a straight line meet two other **straight lines so as to make the two interior angles on the same side of it** together less than two right angles, these two straight lines being continually produced shall at length... | |
| Edward Albert Bowser - 1890 - 393 Seiten
...straight line cut two other straight lines, (1) so as to make the exterior-interior angles equal, or (2) **so as to make the two interior angles on the same side** together equal to two right angles, then the two straight lines are parallel. xE (1) Hyp. Let the st.... | |
| Nikolaĭ Ivanovich Lobachevskiĭ - 1891 - 50 Seiten
...make equal alternate angles, he brings in the un wieldly postulate or axiom: " If a straight line meet **two straight lines, so as to make the two interior...lines, being continually produced, shall at length meet** on that side on which are the angles which are less than two right angles." Do you wonder that succeeding... | |
| Nicholas Murray Butler, Frank Pierrepont Graves, William McAndrew - 1892
...required for use before proposition 14 of his first book. Also the axiom, " If a straight line meet **two straight lines, so as to make the two interior...lines, being continually produced, shall at length meet** on that side on which are the angles which are less than two right angles," is not required till proposition... | |
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